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Imaging modalities such as CT, MRI, and SPECT have had a tremendous impact on diagnosis and treatment planning. These imaging techniques have given doctors the capability to visualize 3D anatomy structures of human body and soft tissues while being non-invasive. Unfortunately, the 3D images produced by these modalities often have boundaries between the organs and soft tissues that are difficult to delineate due to low signal to noise ratios and other factors. Image segmentation is employed as a method for differentiating Regions of Interest in these images by creating artificial contours or boundaries in the images. There are many different techniques for performing segmentation and automating these methods is an active area of research, but currently there are no generalized methods for automatic segmentation due to the complexity of the problem. Therefore hand-segmentation is still widely used in the medical community and is the €œGold standard€� by which all other segmentation methods are measured. However, existing manual segmentation techniques have several drawbacks such as being time consuming, introduce slice interpolation errors when segmenting slice-by-slice, and are generally not reproducible. In this thesis, we present a novel semi-automated method for 3D hand-segmentation that uses mesh extraction and surface parameterization to project several 3D meshes to 2D plane . We hypothesize that allowing the user to better view the relationships between neighboring voxels will aid in delineating Regions of Interest resulting in reduced segmentation time, alleviating slice interpolation artifacts, and be more reproducible.

Le contexte de ma thèse rentre dans le cadre du projet IMD3D, supporté par le FUI. L'objectif de ce projet consiste à proposer une méthode automatisée permettant la décoration d'objets 3D quelconques. La solution choisie consiste à positionner un film imprimé dans le moule, ce film sera déformé par la fermeture du moule puis par injection. Ma thèse porte sur la génération de décoration. Les données dont nous disposons en entrée sont un maillage et une ou plusieurs images. Nous souhaitons d'abord obtenir le plaquage de cette image sur le maillage, de telle sorte que le rendu visuel soit équivalent à l'image initiale. Pour cela, nous avons décidé de choisir un point de vue par image et de le favoriser. Nous paramétrions alors le maillage par le biais d'une projection orthogonale ou perspective définie par ce point de vue. Nous réalisons alors la transformée inverse de déformation du maillage. L'utilisation d'une application conforme pour la déformation inverse permet de coller au mieux à la physique du problème. Nous visualisons donc le résultat à imprimer sur le film. Il reste alors à générer la texture permettant de décorer l'objet injecté par le procédé. Il suffit de parcourir bilinéairement l'intérieur des mailles et simultanément la partie de l'image correspondante, de manière à remplir les pixels de l'image. Ceci permet d'obtenir finalement la texture finale qui sera imprimée sur le film. Mais, lors des premiers essais effectués par les industriels avec une mire colorée, un effet de décoloration a été relevé. Nous avons donc pris en compte ce changement de couleur pour modifier l'image et obtenir le résultat visuel escompte, même au niveau du rendu des couleurs / This work takes part in a global industrial project called IMD3D, which is supported by FUI and aims at decorating 3D plastic objects using Insert Molding technology with an automated process. Our goal is to compute the decoration of 3D virtual objects, using data coming from polymer film characterization and mechanical simulation. My thesis deals with the generation of decoration. Firstly, we want to map the texture onto the mesh, so that the visual rendering would be equivalent to the initial picture. In order to do so, we decided to choose a viewpoint per texture and to favor it. Thus, a specific view-dependent parameterization is defined. Thus, the first goal which is to define the texture mapping with visual constraints is reached. After this step, the inverse distortion of the mesh is performed. The use of a conformal map for this inverse transform allows to respect the physics issues. Therefore we get a planar mesh representing the initial mesh of simulation whose associated textures have also been modified by this transform. The result to be printed on the film can be viewed. Finally, the texture enabling the decoration of the object injected by the process can be generated. This texture combines information from several mapped images. The inner part of the mesh and in the same time the part of the corresponding texture shall be followed in a bilinear way in order to fill the pixel of the generated picture. But during the first tests performed by industries with a colors pattern, a discoloration effect was detected. As a consequence, we thought to take into account this color change to modify the picture and to obtain the expected visual rendering

<p>New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Techniques for computing a high-quality parameterization of the surface are developed and this parameterization is used to approximate the shape of the object. Spherical harmonics are used as basis functions for approximations of the coordinate functions. Information about the global shape is then captured by the coefficients in the spherical harmonics expansions.</p><p>For a starshaped object it is shown how a parameterization can be computed by a projection from its surface onto the unit sphere. An algorithm for computing the position at which the centre of the sphere should be placed, is presented. This algorithm is suited for digital voxel objects. Most of the work is concerned with digital objects whose surfaces are homeomorphic to the sphere. The standard method for computing parameterizations of such surfaces is shown to fail on many objects. This is due to the large distortions of the geometric properties of the surface that often occur with this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are used to find a mapping between a surface and the sphere that minimizes geometric distortion and is useful as a parameterization of the surface. </p><p>The methods can be applied, for example, in medical imaging for shape recognition, detection of shape deformations and shape comparisons of three-dimensional objects.</p>

New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Techniques for computing a high-quality parameterization of the surface are developed and this parameterization is used to approximate the shape of the object. Spherical harmonics are used as basis functions for approximations of the coordinate functions. Information about the global shape is then captured by the coefficients in the spherical harmonics expansions. For a starshaped object it is shown how a parameterization can be computed by a projection from its surface onto the unit sphere. An algorithm for computing the position at which the centre of the sphere should be placed, is presented. This algorithm is suited for digital voxel objects. Most of the work is concerned with digital objects whose surfaces are homeomorphic to the sphere. The standard method for computing parameterizations of such surfaces is shown to fail on many objects. This is due to the large distortions of the geometric properties of the surface that often occur with this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are used to find a mapping between a surface and the sphere that minimizes geometric distortion and is useful as a parameterization of the surface. The methods can be applied, for example, in medical imaging for shape recognition, detection of shape deformations and shape comparisons of three-dimensional objects.

In this thesis work, a 3D Synthetic Human Face Modelling Software is implemented using C++ and OpenGL. B&eacute / zier surfaces, B-spline surfaces, Nonuniform Rational B-spline surfaces, Hierarchical B-Spline surfaces and T-spline surfaces are evaluated as options for the surface description method. T-spline surfaces are chosen since they are found to be superior considering the requirements of the work. In the modelling process, a modular approach is followed. Firstly, high detailed facial regions (i.e. nose, eyes, mouth) are modelled, then these models are unified in a complete face model employing the merging capabilities of T-splines. Local and global features of the face model are parameterized in order to have the ability to create and edit various face models. To enhance the visual quality of the model, a region-variable rendering scheme is employed. In doing this, a new file format to define T-Spline surfaces is proposed. To reduce the computational and memory cost of the software, a simplified version of the T-Spline surface description method is proposed and used.

Afin de convertir un maillage triangulaire en une surface spline de CAGD/CAM, cette thèse adresse l’un des problèmes les plus cruciaux du processus de conversion : extraire un “bon” maillage de contrôle quadrilatéral de la surface. Ce que nous entendons par “bon” est que les arêtes du maillage de contrôle se croisent perpendiculairement et sont alignées avec les principales directions de la courbure de la surface. Ces deux propriétés du maillage de contrôle permettent de fournir une bonne approximation de la surface avec peu de points de contrôles. D’ailleurs, ils aident considérablement à réduire des oscillations non désirées sur la surface spline finale. Pour résoudre ce problème, nous proposons un nouvel algorithme automatique, appelé paramétrisation globale périodique. L’idée fondamentale de cet algorithme est de trouver une paramétrisation qui ait un “sens d’un point de vue géométrique”, pour ce faire, elle doit être guidée par la courbure de la surface, représentée par une paire de champs de direction orthogonaux. Les iso-lignes de cette paramétrisation sont ensuite extraites pour définir un maillage de contrôle qui ait les propriétés requises. Ce maillage de contrôle, nous permet de construire une approximation en surface T-spline de la surface triangulée initiale. Nous exposons plusieurs résultats de cette conversion d’un maillage triangulée en surface spline. Les résultats montrent que, grâce aux maillages de contrôle anisotropes, les surfaces spline finales ont beaucoup moins d’oscillations que celles construites par les méthodes précédentes qui ne tiennent pas compte de l’anisotropie de la surface / Aiming at converting a triangular mesh into a CAGD/CAM spline surface, this thesis focuses on one of the most crucial problems of the conversion process, i.e. extracting a “good” quadrilateral control mesh of the surface. What we mean by good is that the edges of the control mesh should be orthogonal and aligned with the principal directions of curvature of the surface. These two properties make the control mesh optimum in an approximation point of view, and greatly help to reduce unwanted oscillations on the final spline surface built from it. To solve this problem, we propose a new automatic algorithm, called periodic global parameterization. The basic idea is to find a “geometry-meaningful” parameterization guided by a pair of orthogonal anisotropic direction fields. Then, the iso-value lines of this parameterization will be extracted to define an initial control mesh, that satisfies the two criteria of a good control mesh. With the initial control mesh, we explain how to construct a T-spline approximation of the initial triangulated surface. We show several examples of the triangular mesh to T-spline conversion. The results show that thanks to the anisotropic control meshes, the final spline surfaces generated have much less oscillations as compared to results of previous methods, that do not take into account of the anisotropy

Natural surfaces are usually associated with feature graphs, such as the cortical surface with anatomical atlas structure. Such a feature graph subdivides the whole surface into meaningful sub-regions. Existing brain mapping and registration methods did not integrate anatomical atlas structures. As a result, with existing brain mappings, it is difficult to visualize and compare the atlas structures. And also existing brain registration methods can not guarantee the best possible alignment of the cortical regions which can help computing more accurate shape similarity metrics for neurodegenerative disease analysis, e.g., Alzheimer’s disease (AD) classification. Also, not much attention has been paid to tackle surface parameterization and registration with graph constraints in a rigorous way which have many applications in graphics, e.g., surface and image morphing. This dissertation explores structural mappings for shape analysis of surfaces using the feature graphs as constraints. (1) First, we propose structural brain mapping which maps the brain cortical surface onto a planar convex domain using Tutte embedding of a novel atlas graph and harmonic map with atlas graph constraints to facilitate visualization and comparison between the atlas structures. (2) Next, we propose a novel brain registration technique based on an intrinsic atlas-constrained harmonic map which provides the best possible alignment of the cortical regions. (3) After that, the proposed brain registration technique has been applied to compute shape similarity metrics for AD classification. (4) Finally, we propose techniques to compute intrinsic graph-constrained parameterization and registration for general genus-0 surfaces which have been used in surface and image morphing applications.

Ce mémoire s'inscrit dans le domaine de la vision par ordinateur. Elle s'intéresse à la calibration de systèmes de caméras stéréoscopiques, à la mise en correspondance caméra-projecteur, à la reconstruction 3D, à l'alignement photométrique de projecteurs, au maillage de nuages de points, ainsi qu'au paramétrage de surfaces. Réalisé dans le cadre du projet LightTwist du laboratoire Vision3D, elle vise à permettre la projection sur grandes surfaces arbitraires à l'aide de plusieurs projecteurs. Ce genre de projection est souvent utilisé en arts technologiques, en théâtre et en projection architecturale. Dans ce mémoire, on procède au calibrage des caméras, suivi d'une reconstruction 3D par morceaux basée sur une méthode active de mise en correspondance, la lumière non structurée. Après un alignement et un maillage automatisés, on dispose d'un modèle 3D complet de la surface de projection. Ce mémoire introduit ensuite une nouvelle approche pour le paramétrage de modèles 3D basée sur le calcul efficace de distances géodésiques sur des maillages. L'usager n'a qu'à délimiter manuellement le contour de la zone de projection sur le modèle. Le paramétrage final est calculé en utilisant les distances obtenues pour chaque point du modèle. Jusqu'à maintenant, les méthodes existante ne permettaient pas de paramétrer des modèles ayant plus d'un million de points. / This thesis falls within the field of computer vision. It focuses on stereoscopic camera calibration, camera-projector matching, 3D reconstruction, projector blending, point cloud meshing, and surface parameterization. Conducted as part of the LightTwist project at the Vision3D laboratory, the work presented in this thesis aims to facilitate video projections on large surfaces of arbitrary shape using more than one projector. This type of projection is often seen in theater, digital arts, and architectural projections. To this end, we begin with the calibration of the cameras, followed by a piecewise 3D reconstruction using an active unstructured light scanning method. An automated alignment and meshing of the partial reconstructions yields a complete 3D model of the projection surface. This thesis then introduces a new approach for the parameterization of 3D models based on an efficient computation of geodesic distances across triangular meshes. The only input required from the user is the manual selection of the boudaries of the projection area on the model. The final parameterization is computed using the geodesic distances obtained for each of the model's vertices. Until now, existing methods did not permit the parameterization of models having a million vertices or more.